4 problems

Let $G$ be a relatively hyperbolic diagram group. Free-product conjecture. Relatively hyperbolic diagram groups are free products. The claim gives a more precise form of the preced…

Let $G$ be a diagram group, and let $\mathbb{Z} \wr \mathbb{Z}^2$ denote the wreath product of $\mathbb{Z}$ by $\mathbb{Z}^2$. Lamplighter exclusion conjecture. The group $G$ does…

Let $\mathcal{K}$ be a directed $2$-complex, let $u$ be a $1$-path, and let $H$ be a subgroup of the diagram group $\mathrm{DG}(\mathcal{K},u)$. A subgroup is closed for components…

Let $D(\mathcal{P},w)$ be a diagram group, and let $A(\mathcal{P},w)$ denote the associated right-angled Artin group. A diagram group is embeddable into a right-angled Artin group…